Mass, Weight, Density, and Pressure

In some textbooks you'll find mass defined as "amount of stuff" or "amount of a particular material." Other books will define mass as inertia or as resistance to change in motion (this comes from Newton's 2nd law of motion, somthing we'll cover that later in the semester). The next picture illustrates both these definitions. A Cadillac and a volkswagen have both stalled in an intersection. Both cars are made of steel. The Cadillac is larger and has more steel, more stuff, more mass. The Cadillac will be harder to get moving than the VW, it has a larger inertia (the Cadillac would also be harder to slow down, once it is moving, than the Volkswagen).

Weight is a force and depends on both the mass of an object and the strength of gravity. We tend to use weight and mass interchangeably because we spend all our lives on the earth where gravity never changes.

On the earth where the pull of gravity never changes, any three objects that all have the same mass (even if they have different volumes and are made of different materials) would always have the same weight. There is quite a bit of information hidden in the gravitational acceleration term. Click here for more details.

Conversely:When gravity is always the same, three objects with the same weight would also have the same mass.

The difference between mass and weight is clearer (perhaps) if you compare the situation on the earth and on the moon.

An object carried from the earth to the moon will have the same mass. However the gravitational attraction between the object and the moon is less than on the earth. So the object weighs less on the moon than it does on the earth.

Air density will come up frequently in this class. Density is defined as mass divided by volume.

In the first example there is more mass (more dots) in the right box than in the left box. Since the two volumes are equal the box at right has higher density. Equal masses are squeezed into different volumes in the bottom example. The box with smaller volume has higher density.

Pressure is defined as force divided by area. Air pressure is the weight of the atmosphere overhead divided by the area the air is resting on. Atmospheric pressure is determined by and tells you something about the weight of the air overhead. This is one way, a sort of large scale representation, of understanding air pressure.

Under normal conditions a 1 inch by 1 inch column of air stretching from sea level to the top of the atmosphere will weigh 14.7 pounds. Normal atmospheric pressure at sea level is 14.7 pounds per square inch (psi, the units you use when you fill up your car or bike tires with air).

A steel bar (52"x1"x1") weighs exactly 14.7 pounds Steel is a lot denser than air, so a steel bar only needs to be 52 inches tall to have the same weight as an air column that is 100 miles or more tall. Because the base of the bar has dimensions of 1" x 1" (1 square inch) the pressure at the bottom of the bar is 14.7 psi. A stack of ninety four 5 pound bricks would weigh 470 pounds. The pile of bricks is much heavier but it is also sitting on a much larger area. The pressure at the base of the brick pile would be 470 pounds divided by 32 square inches (the side of a brick has dimensions of about 4 x 8 inches) or about 14.7 psi.

Here are some of the other commonly used pressure units.

Typical sea level pressure is 14.7 psi or about 1000 millibars (the units used by meterologists and the units that we will use in this class most of the time) or about 30 inches of mercury (refers to the reading on a mercury barometer).

The word "bar" basically means pressure and is used in a lot of meteorological terms.

Pressure at sea level is determined by the weight of the air overhead.What happens to pressure as you move upward in the atmosphere. We can use a shorter pile of bricks to help answer this question. You can think of the bricks representing layers of air in the atmosphere.

Each brick weighs 5 pounds. At the bottom of the 5 brick tall pile you would measure a weight of 25 pounds. If you moved up a brick you would measure a weight of 20 pounds, the weight of the four bricks still above. To get the pressure you would need to divide by the area. It should be clear that weight and pressure will decrease as you move up the pile.

In the atmosphere, pressure at any level is determined by the weight of the air still overhead. Pressure decreases with increasing altitude because there is less and less air remaining overhead.

At sea level altitude, at Point 1, the pressure is normally about 1000 mb. That is determined by the weight of all (100%) of the air in the atmosphere.

Some parts of Tucson, at Point 2, are 3000 feet above sea level (most of the valley is a little lower than that, around 2500 feet). At 3000 ft. about 10% of the air is below, 90% is still overhead. It is the weight of the 90% that is still above that determines the atmospheric pressure in Tucson. If 100% of the atmosphere produces a pressure of 1000 mb, then 90% will produce a pressure of 900 mb.

Pressure is typically about 700 mb at the summit of Mt. Lemmon (9000 ft. altitude at Point 3) and 70% of the atmosphere is overhead..

Pressure decreases rapidly with increasing altitude. We will find that pressure changes more slowly if you move horizontally. But the small horizontal changes are what cause the wind to blow and what cause storms to form.

Point 4 shows a submarine at a depth of about 30 ft. The pressure there is determined by the weight of the air and the weight of the water overhead. Water is much denser and much heavier than air. At 33 ft., the pressure is already twice what it would be at the surface of the ocean (2000 mb instead of 1000 mb).

Air pressure decreases with increasing altitude. The rate of pressure decrease depends on the air density. Pressure decreases most rapidly with increasing altitude in high density air.

There is a lot going on in this figure.

Point 1 - Notice there is a 100 mb drop in pressure in both air layers. In order for this to be true both layers must have the same weight. In order for both layers to have the same weight they must contain the same amount of air, they have the same mass.

Point 2a - The pressure decreases 100 mb in a relatively short distance. This produces a relatively rapid rate of pressure decrease with increasing altitude.
Point 2b - The pressure also decreases 100 mb but in a longer distance. Pressure is decreasing at a slower rate in this layer.

Point 3 - The in the left layer is denser than the air in the right layer. The same amount of air is squeezed into a thinner layer, a smaller volume, in the left layer. This results in relatively high density air.

The fact that the rate of pressure decrease with increasing altitude depends on air density is a fairly subtle but important concept. This concept will come up 2 or 3 more times later in the semester. For example, we will use this concept to explain why hurricanes can intensify and get as strong as they do.

Mercury barometers are used to measure atmospheric pressure. A mercury barometer is really just a balance that can be used to weigh the atmosphere.

The instrument in the left figure above ( a u-shaped glass tube filled with a liquid of some kind) is actually called a manometer and can be used to measure pressure difference. The two ends of the tube are open so that air can get inside and air pressure can press on the liquid. Given that the liquid levels on the two sides of the manometer are equal, what could you about PL and PR?

The liquid can slosh back and forth just like the pans on a balance can move up and down. A manometer really behaves just like a pan balance (pictured at right). Because the two pans are in balance, the two columns of air have the same weight.

PL and PR are equal (note you don't really know what either pressure is, just that they are equal).

Now the situation is a little different, the liquid levels are no longer equal. You probably realize that the air pressure on the left, PL, is a little higher than the air pressure on the right, PR. PL is now being balanced by PR + P acting together. P is the pressure produced by the weight of the extra fluid on the right hand side of the manometer (the fluid that lies above the dotted line). The height of the column of extra liquid provides a measure of the difference between PL and PR.

Next we will just go and close off the right hand side of the manometer.

Air pressure can't get into the right tube any more. Now at the level of the dotted line the balance is between Pair and P (pressure by the extra liquid on the right). If Pair changes, the height of the right column, h, will change. You now have a barometer, an instrument that can measure and monitor the atmospheric pressure. (some of the letters were cut off in the upper right portion of the left figure, they should read "no air pressure")

Barometers like this are usually filled with mercury. Mercury is a liquid. You need a liquid that can slosh back and forth in response to changes in air pressure. Mercury is also very dense which means the barometer won't need to be as tall as if you used something like water. A water barometer would need to be over 30 feet tall. With mercury you will need only a 30 inch tall column to balance the weight of the atmosphere at sea level under normal conditions (remember the 30 inches of mercury pressure units mentioned earlier). Mercury also has a low rate of evaporation so you don't have much mercury gas at the top of the right tube (it is the mercury vapor that would make a mercury spill in the classroom dangerous).

Here is a more conventional barometer design. The bowl of mercury is usually covered in such a way that it can sense changes in pressure but not evaporate and fill the room with poisonous mercury vapor.

The figure above first shows average sea level pressure values. 1000 mb or 30 inches of mercury are close enough in this class.

Sea level pressures usually fall between 950 mb and 1050 mb.

Most of the record low pressure values have all been set by intense hurricanes (the extreme low pressure is the reason these storms are so intense). Hurricane Wilma in 2005 set a new record low sea level pressure reading for the Atlantic, 882 mb. Hurricane Katrina had a pressure of 902 mb. The following table lists some information on strong hurricanes that have affected the US. Three of the 10 strongest N. Atlantic hurricanes occurred in 2005, the year Katrina hit New Orleans.

Note that a new all time record low sea level pressure was measured in 2003 inside a strong tornado in Manchester, South Dakota (F4 refers to the Fujita scale rating, F5 is the highest level on the scale). This is very difficult (and potentially very dangerous) thing to do. Not only must the instruments be built to survive a tornado but they must also be placed on the ground ahead of an approaching tornado and the tornado must then pass over the instruments.

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